September 1998

NASA/TP-1998-208464

A Method for Integrating Thrust-Vectoring andActuated Forebody Strakes With ConventionalAerodynamic Controls on a High-PerformanceFighter Airplane

Frederick J. Lallman, John B. Davidson, and Patrick C. MurphyLangley Research Center, Hampton, Virginia

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September 1998

NASA/TP-1998-208464

A Method for Integrating Thrust-Vectoring andActuated Forebody Strakes With ConventionalAerodynamic Controls on a High-PerformanceFighter Airplane

Frederick J. Lallman, John B. Davidson, and Patrick C. MurphyLangley Research Center, Hampton, Virginia

Available from the following:

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iii

Contents

Summary ....................................................................................................................................................... 1

Introduction................................................................................................................................................... 2

Symbols and Nomenclature .......................................................................................................................... 7

Pseudo Controls Overview ......................................................................................................................... 10

Controls Interconnect .................................................................................................................................. 11

Axis Transformation............................................................................................................................. 12

Moment Commands ............................................................................................................................. 12

Pseudo Control Variables..................................................................................................................... 12

Roll Acceleration.................................................................................................................................. 13

Controls Distribution................................................................................................................................... 14

Distribution of Conventional Controls ................................................................................................. 14

Control Moments – Conventional Controls ................................................................................... 14Distribution Schedule Calculations................................................................................................ 16Distribution Schedules ................................................................................................................... 17Conventional Controls Coefficients............................................................................................... 18

Distribution of Thrust-Vectoring Controls ........................................................................................... 20

Distribution of Actuated Forebody Strake Controls ............................................................................. 21

Actuated Forebody Strake Dead-Band .......................................................................................... 21Actuated Forebody Strake Calibration........................................................................................... 22

Controls Coordination .......................................................................................................................... 24

Accelerometer Correction .................................................................................................................... 24

Thrust-Vectoring Engagement.................................................................................................................... 26

Thrust-Vectoring Schedules ................................................................................................................. 27

Thrust-Vectoring Envelopes................................................................................................................. 29

Vane Relief ................................................................................................................................................. 31

General Design ..................................................................................................................................... 32

Filter Time Constant............................................................................................................................. 35

Simulation Example ............................................................................................................................. 36

Concluding Remarks................................................................................................................................... 37

References ................................................................................................................................................... 38

1

Abstract

A method, called pseudo controls, of integrating several airplanecontrols to achieve cooperative operation is presented. The methodeliminates conflicting control motions, minimizes the number of feedbackcontrol gains, and reduces the complication of feedback gain schedules.The method is applied to the lateral/directional controls of a modifiedhigh-performance airplane. The airplane has a conventional set ofaerodynamic controls, an experimental set of thrust-vectoring controls,and an experimental set of actuated forebody strakes. The experimentalcontrols give the airplane additional control power for enhancedstability and maneuvering capabilities while flying over an expandedenvelope, especially at high angles of attack.

The flight controls are scheduled to generate independent body-axiscontrol moments. These control moments are coordinated to producestability-axis angular accelerations. Inertial coupling moments arecompensated. Thrust-vectoring controls are engaged according to theireffectiveness relative to that of the aerodynamic controls. Vane-relieflogic removes steady and slowly varying commands from the thrust-vectoring controls to alleviate heating of the thrust turning devices. Theactuated forebody strakes are engaged at high angles of attack.

This report presents the forward-loop elements of a flight controlsystem that positions the flight controls according to desired stability-axis accelerations. This report does not include the generation of therequired angular acceleration commands by means of pilot controls orthe feedback of sensed airplane motions.

Summary

The pseudo controls method for integrating lateral/directional aerodynamic and thrust-vectoringcontrols on fighter-type jet airplanes is presented. The NASA High-Alpha Research Vehicle (HARV)discussed in this report is a modern high-performance twin-engine jet fighter that is modified to carry anexperimental thrust-vectoring apparatus and an experimental set of actuated forebody strakes. Theexperimental controls augment the conventional aerodynamic controls (ailerons, twin rudders, and ahorizontal stabilator capable of differential deflections) to extend the flight envelope to high angles ofattack and slow airspeeds.

The purpose of the pseudo controls method is to integrate the conventional aerodynamic controls withexperimental thrust-vectoring and actuated forebody strake controls. The pseudo controls methodorganizes the aerodynamic and thrust-vectoring control activity to cause moments about the airplane axesthat satisfy the demands of stability augmentation feedback loops, pilot commands, and inertialdecoupling. The pseudo controls method converts stability-axis roll and yaw angular accelerationcommands into coordinated control deflections. This reduces the number of commanded items from thenumber of controls available to commanded roll and yaw accelerations and simplifies the task of thedesigner of the feedback part of the control system. The acceleration commands are generated from pilotcontrol inputs and stabilizing feedback sensor signals. This may be accomplished by any acceptedcontrol law design method and is not addressed in this report. The acceleration commands are distributed

2

to the control effectors in proportions that are scheduled according to flight conditions. Distribution gainsare determined for the conventional controls to separate body-axis rolling and yawing control moments.The thrust-vectoring and actuated forebody strake controls are specifically designed to generate momentsabout the body axes. The actuated forebody strakes engage when the angle of attack is at least20 degrees. Thrust-vectoring controls engage when their control moment producing capabilities arecomparable to that of the aerodynamic controls. The conventional aerodynamic control deflections areadjusted to compensate for the increased control power made available by the thrust-vectoring andactuated forebody strake controls. To minimize heating of the thrust-turning vanes, a vane reliefalgorithm was developed to replace steady thrust-vectoring commands by increased deflections of theaerodynamic controls.

The development of the pseudo controls method and its application to the HARV airplane as describedin this report were performed under the NASA High-Alpha Technology Program (HATP).

Introduction

One key element in the evolution of fighter airplane designs into more effective configurations is theability to fly at increasing angles of attack. New types of control devices allow flight operations that arebeyond the reach of conventional airplanes. Vectored thrust and forebody controls can provide controlpower to maintain stable and effective flight in the post-stall regime. Control system designs using thesenew, effective devices can provide safe maneuverability at post-stall angles of attack with inherentdeparture and spin resistance. In addition, the availability of control power during post-stall flight createsnew opportunities for gaining tactical advantage over an adversary.

A number of airplanes have achieved controlled flight in the post-stall regime. The Grumman AircraftCorporation X-29 Forward Swept Wing Technology Demonstrator airplane achieved controlled flight atpost-stall angles of attack because of its unique wing design and close-coupled canards (reference 1). TheRockwell International Corporation’s North American Aircraft & Deutsche Aerospace (formerlyMesserschmitt-Bolkow-Blohm) X-31 Enhanced Fighter Maneuverability Demonstrator, the LockheedFort Worth Company F-16 Multi-Axis Thrust Vectoring (MATV), and the Lockheed AdvancedDevelopment Company, The Boeing Company & General Dynamics YF-22 Advanced Tactical Fighterprototype (reference 2) have reached angles of attack of 60° or more because of their use of thrust-vectoring controls. Another airplane that has flown these high angles of attack is the NationalAeronautics and Space Administration (NASA) F-18 High Angle-of-Attack Research Vehicle (HARV).The HARV airplane (figure 1) flew in support of the NASA High-Angle-of-Attack Technology Program(HATP). HATP was a technology development and validation program for fighter airplanes possessinghigh angle-of-attack maneuverability and controllability (reference 3). The program used analysis,ground-based testing, simulation, and flight tests to advance technology in aerodynamics, advancedcontrols, and maneuver management. The HARV airplane achieved controlled flight up to 60 degreesangle of attack and was the first airplane to use active forebody controls (actuated strakes) to enhancerolling maneuvers. The present report describes a method of integrating new post-stall control effectorswith conventional aerodynamic controls that was part of an experimental high angle-of-attack flightcontrol system developed for HARV.

The HATP program used the HARV as a flight test vehicle to validate high angle-of-attack controldesigns and to gather flight test data. The HARV airplane was a full-scale developmental twin-engine,single-place, fighter/attack (F/A) airplane. It was built for the US Navy by the McDonnell Douglas Corp.

3

Figure 1. The High Angle-of-Attack Research Vehicle (HARV).1

(St. Louis, MO) and the Northrop Corp. (Newbury Park, CA) and was previously used for high angle ofattack and spin testing. The HARV was powered by two General Electric (Lynn, MA) F404-GE-400afterburning turbofan engines.

Several modifications were made to the airplane to prepare it for flight tests (references 4 and 5). Aresearch flight control system (RFCS) using Pace 1750A computers (Performance Semiconductor Corp.,Sunnyvale, CA) was added to the airplane avionics. Research control laws and flight test software wereprogrammed in the RFCS computers. An emergency spin recovery parachute assembly was mounted tothe upper aft portion of the airplane between the engines. High angle-of-attack in-flight flowvisualization and pressure measurement equipment was installed. Flight-test instrumentation and real-time air-to-ground data links were installed. Various indicators, switches, etc., were provided in thecockpit to allow the pilot to monitor and control the special flight test equipment.

Turning vanes were added to the HARV to provide thrust-vectoring capability (figure 2). In order toaccommodate the vane installation, the engines were modified by removing the divergent flap portion ofthe nozzle. The convergent nozzle hardware was modified to maintain structural integrity and the enginecontroller was modified to increase the engine stall margin. The inside trailing edges of the stabilatorswere modified slightly to provide clearance for the thrust-vectoring hardware.

Three vanes were positioned about the periphery of each engine nozzle. The vanes were made ofInconel 625® steel and each was moved by a modified aileron electrohydraulic actuator. The larger topvanes generate nose-down pitching moments, while the smaller lower (inboard and outboard) vanesmoved collectively to generate nose-up pitching moments. Other combinations of vane positions weredesigned to cause the generation of yaw and rolling moments.

In order to initially evaluate the vectoring capability and isolated nozzle performance of the thrust-vectoring system, a static (wind-off) test was conducted on a 14.25 percent scaled model. Vane sizes andactuation geometries were tested over a range of deflections and nozzle pressure ratios with military-power and afterburning-power nozzles. The test examined the effects of vane deflections on thrustvectoring and resultant thrust losses. The test results favored the simple rotating vane actuation systemthat was implemented on the HARV airplane over a more complicated translating-rotating vane concept(reference 6).

1Photographs supplied by NASA Dryden Flight Research Center, Edwards, CA.®Inconel 625 is a registered trademark of Huntington Alloy Products Division, International Nickel Co.,Huntington, WV.

4

Figure 2. HARV Thrust-Vectoring System.

A wingtip-supported, partially metric, 0.10-scale (cold) jet-effects model of an F-18 prototype aircraftwas modified with hardware to simulate the thrust-vectoring control system of the HARV. Afterbodyaerodynamic and thrust-vectoring forces and moments were measured at free-stream Mach numbersranging from 0.30 to 0.70, at angles of attack from 0° to 70°, and at nozzle pressure ratios from 1.0 to 5.0with afterburning and military power nozzles (reference 7). These data were used to design aMixer/Predictor program that could position the vanes to get commanded pitch, yaw, and roll moments(reference 8). The HARV experiments used pitch and yaw thrust-vectoring moments to maintain stableflight at high angles of attack. The roll thrust-vectoring capability was not used in the flight test programbecause the roll moments produced were limited by priority logic in the Mixer/Predictor program.Figure 3 shows the thrust-vectoring system deflecting engine thrust during a propulsion system test.

Figure 3. HARV Thrust Vectoring Test.

The HARV airplane initially flew with thrust-vectoring controls during 1991. A flight test programestablished the utility of thrust-vectoring controls and demonstrated controlled, maneuvering flight atpost-stall angles of attack. The flight control law used at that time was developed jointly by NASA andMcDonnell Aircraft Company. A second thrust-vectoring control law, known as the NASA-1A control

5

law, was developed at NASA Langley Research Center. The NASA-1A control law was flown on theHARV during 1994.

The radome of the HARV was replaced with a specially built radome that includes a pair of longitudi-nally hinged, actuated forebody strakes (reference 9). Deployment of the strakes (figure 4) changes theflow separation and vortices shed from the airplane forebody when flying at high angles of attack. Wind-tunnel tests predicted that the yawing moments resulting from differential strake deflections wouldprovide a powerful means of controlling the HARV at high angles of attack (references 9 and 10).

Figure 4. HARV Airplane with Left Actuated Forebody Strake Deployed.

The radome and actuated forebody strake structures consisted of aluminum skin panels riveted toaluminum stringers and bulkheads. The strakes were moved by F-18 aileron actuators modified forlonger strokes and faster rates. When closed (0° deflection), the strakes conformed to the normal shape ofthe F-18 radome. The strakes could be independently commanded up to 90° deflections within1/2 second.

Flight control laws that used the actuated forebody strakes and the thrust-vectoring system weredeveloped at NASA Langley Research Center and are known as the ANSER (Actuated Nose Strakes forEnhanced Rolling) Control Laws. A detailed specification of the ANSER control law is given in refer-ence 11. The control laws were tailored to satisfy a number of performance and handling quality designguidelines (reference 12). The ANSER control law used a “mixer-predictor” to position the thrust-vectoring vanes in response to multiaxis thrust-vector angle commands (reference 8). A longitudinalcontroller consisted of a variable-gain output-feedback controller, a feed-forward command generator,and a command generator tracker (reference 13). The longitudinal controller used horizontal tail

6

deflections and pitch-axis thrust vectoring to achieve rapid (agile) pitching motions to commanded anglesof attack. The leading-edge and trailing-edge flaps follow the schedules of the production F/A-18airplane. The lateral/directional controller used stability-axis roll and yaw angular accelerations tocontrol stability-axis roll rate and sideslip angle. Feedback control gain schedules were calculated usingdirect eigenspace assignment with tradeoffs among control power, robustness, agility, and flying qualitiesmetrics (reference 14). The control laws were programmed in the FORTRAN programming language forground-based testing. A simulation program of a baseline F/A-18 airplane (reference 15) was modified torepresent the HARV airplane including the TVCS and ANSER controls (reference 16). Testing of theseprograms was performed by an ACSL (Advanced Continuous Simulation Language, reference 17) batch-mode simulation. Piloted evaluation of the HARV airplane and the ANSER control laws was conductedin the Differential Maneuvering Simulator (DMS) at NASA Langley Research Center (reference 18).The DMS is a fixed-based simulator having wide-angle visual displays and is capable of simulating twoairplanes as they maneuver relative to each other. The evaluations used a series of piloting tasks designedto test the longitudinal and the lateral/directional control systems throughout the HARV flight envelope(reference 12). The ANSER control laws were installed in the RFCS computers onboard the HARVairplane and hardware-in-the-loop simulations at NASA Dryden Flight Research Facility. The flight testswere designed to provide aerodynamic measurements, flow field visualizations, airplane controllability,and agility ratings. These flight tests were conducted from 1995 to 1996 at NASA Dryden FlightResearch Facility.

One challenge of the ANSER control system was to determine how to best schedule the many controleffectors, especially at high angles of attack. The organization of these controls to provide independentchannels of control of lateral and directional motions throughout the flight test envelope wasaccomplished by using the pseudo controls method. An early version of the pseudo controls method isdescribed in references 19 and 20 for a jet fighter configuration having roll and yaw thrust-vectoringcapabilities in addition to ailerons, rudder, and differential horizontal tail available for control. Thecontrols were coordinated to form one control channel that affected the Dutch roll mode and anotherchannel that affected the roll and spiral modes of the airplane (reference 19). This method was appliedover a range of trimmed, level flight conditions to produce schedules that distributed the individualchannel commands among the four control effectors. Feedback loops were added and batch simulationresults demonstrated promising results. Lateral control stick deflections caused stability-axis roll rateswith small Dutch roll excitation and rudder pedal deflections caused steady sideslips with small steady-state roll rates (reference 20).

The pseudo controls method was applied to the mathematical model of the HARV airplane as a way ofcoordinating all its lateral/directional controls and reducing the number of feedback control channels. Forthe HARV airplane, an envelope was defined over a wide range of angle of attack, Mach number, andengine thrust settings without reference to trimmed flight. Unfortunately, the calculated distributions werevery sensitive at some conditions and it was felt that the scheduling of the results of the early pseudocontrols method would be impractical for the HARV airplane. The pseudo controls method was modifiedfor use on the HARV airplane. The lateral and directional control channels were configured to producestability-axis accelerations instead of affecting the dynamic modes of motion as was previouslyattempted. The remainder of this report provides a detailed description of the modified pseudo controlsmethod as it was implemented on the HARV airplane.

7

Symbols and Nomenclature

Numerical values, where given, are nominal values for the HARV airplane.

Symbol Value Unit Description

ANSER  –   –  Actuated Nose Strakes for Enhanced Rolling

AOA  –   degree  angle of attack 

 ay   –   ft/sec2  lateral acceleration at the sensor location 

acg  –   ft/sec2  lateral acceleration at the center of gravity 

ay,corr  –   ft/sec2  lateral accelerometer correction 

ay,TV  –  ft/sec2

per ft-lbinterference of thrust vectoring on lateralaccelerometer

ay,FS  –  ft/sec2

per ft-lbinterference of actuated forebody strakes on lateralaccelerometer

b  37.42   ft  wing span 

croll →  –   ft-lb  3-vector of roll moments 

cyaw →  –   ft-lb  3-vector of yaw moments 

d→  –   –  solution of optimization problem 

c.g.  –   –  center of gravity 

Clδa  –   deg−1  aileron roll control derivative 

Clδd  –   deg−1  differential tail roll control derivative 

Clδr  –   deg−1  rudder roll control derivative 

Cnδa  –   deg−1  aileron yaw control derivative 

Cnδd  –   deg−1  differential tail yaw control derivative 

Cnδr  –   deg−1  rudder yaw control derivative 

Croll – – aerodynamic roll moment coefficient availablefrom conventional controls

Cyaw – – aerodynamic yaw moment coefficient availablefrom conventional controls

CRAFT Control power, Robustness, Agility, and Flyingqualities Tradeoffs

droll

→  –   –  roll distribution 3-vector 

dyaw →  –   –  yaw distribution 3-vector 

Faero – pound lateral aerodynamic force including conventionalcontrols

FFS  –  pound lateral force of actuated forebody strakes

FTV  –  pound lateral thrust-vectoring force

HARV  –   –  High-Angle-of-Attack Research Vehicle 

8

Symbol Value Unit Description

HATP  –   –  High-Alpha Technology Program 

IXX 22 632  slug-ft2  moment of inertia (roll axis)

IXZ –2131.8  slug-ft2  product of inertia

IYY 174 246.3  slug-ft2  moment of inertia (pitch axis)

IZZ 189 336.4  slug-ft2  moment of inertia (yaw axis)

J –  (ft-lb)2  performance index for optimization problem

KEAS – knots knots equivalent airspeed

L – ft-lb roll control moment

Laero – ft-lb aerodynamic roll moment available fromconventional controls

Lavail – ft-lb available roll control moment for vroll = 1

Lcmd – ft-lb commanded roll control moment

LTV – ft-lb available roll thrust-vector control moment

la 12.46 ft distance from c.g. to lateral accelerometer

lFS – ft effective forebody strake moment arm

lTV 20.3 ft distance from c.g. to the TV nozzles

ly 1.53 ft lateral distance from centerline to nozzles

lz 0.45 ft distance TV nozzles below c.g.

M – ft-lb total control moment §

MA – ft-lb available aerodynamic control moment §

MC – ft-lb commanded control moment §

MTV – ft-lb available thrust-vectoring control moment §

m 1111.6 slug mass of airplane

N – ft-lb yaw control moment

Naero – ft-lb aerodynamic yaw moment available fromconventional controls

Navail – ft-lb available yaw control moment for vyaw = 1

Ncmd – ft-lb commanded yaw control moment

NFS – ft-lb commanded actuated forebody strake yaw controlmoment

NTV – ft-lb available yaw thrust-vector control moment

p – rad/sec body-axis roll rate

pcmd – rad/sec2 commanded body-axis roll acceleration

˙ maxp –  rad/sec2  body-axis roll acceleration capability

ps –  rad/sec2  stability-axis roll acceleration

§variable may refer to either roll or yaw axis depending on application.

9

Symbol Value Unit Description

˙ ,maxps –  rad/sec2  maximum stability-axis roll acceleration

q – rad/sec body-axis pitch rate

q –  lb/ft2  dynamic pressure

r – rad/sec body-axis yaw rate

r –  rad/sec2  body-axis yaw acceleration

rcmd – rad/sec2 commanded body-axis yaw acceleration

˙maxr –  rad/sec2  body-axis yaw acceleration capability

rs –  rad/sec2  stability-axis yaw acceleration

S 400  ft2  reference wing area

STV 0 to 1 – thrust-vectoring engagement variable

STVr 0 to 1 – roll TV engagement variable

STVy 0 to 1 – yaw TV engagement variable

T – lb total engine thrust

Tc – sec vane relief filter time constant §

TED – – trailing edge down

TEU – – trailing edge up

TV – – Thrust Vector

u→ – – 3-vector of normalized control deflections

V – ft/sec velocity

vA –1 to +1 – aerodynamic pseudo control variable §

vA,nom –1 to +1 – nominal aerodynamic pseudo control variable §

vC –1 to +1 – command pseudo control variable §

vdir –  rad/sec2  directional pseudo control variable

vlat –  rad/sec2  lateral pseudo control variable

vroll –1 to +1 – roll pseudo control variable

vTV –1 to +1 – thrust-vectoring pseudo control variable §

vTV,nom –1 to +1 – nominal thrust-vectoring pseudo control variable §

vyaw –1 to +1 – yaw pseudo control variable

W – (ft-lb)2 (3×3) matrix (products of moment coefficients)

α – degree angle of attack

∆Clδa – – roll moment coefficient for maximum ailerondeflection

∆Clδd – – roll moment coefficient for maximum differentialstabilator deflection

§variable may refer to either roll or yaw axis depending on application.

10

Symbol Value Unit Description

∆Clδr – – roll moment coefficient for maximum rudderdeflection

∆Cnδa – – yaw moment coefficient for maximum ailerondeflection

∆Cnδd – – yaw moment coefficient for maximum differentialstabilator deflection

∆Cnδr – – yaw moment coefficient for maximum rudderdeflection

∆Cn,FS – – yaw moment coefficient for maximum actuatedforebody strake deflection

∆vΑ ±1 – aerodynamic vane relief increment §

∆vΑ,filt ±1 – filtered aerodynamic vane relief increment §

δa – degree aileron deflection angle

δam 25.0 degree maximum aileron deflection angle

δd – degree differential tail deflection angle

δdm 17.25* degree maximum differential tail deflection angle

δFS ±90.0 degree maximum differential actuated forebody strakedeflection

δr – degree rudder deflection angle

δrm 30.0 degree maximum rudder deflection angle

δTVr – degree rolling thrust-vector angle

δTVrm 15.0 degree maximum rolling thrust-vector angle

δTVy – degree yawing thrust-vector angle

δTVym 10.0 degree maximum yawing thrust-vector angle

§variable may refer to either roll or yaw axis depending on application.*each horizontal tail surface deflects from –24.0 to +10.5 degrees.

Pseudo Controls Overview

This section presents a brief overview of the integrated lateral/directional controls system designed forthe HARV airplane. The system as shown in figure 5 is partitioned into a feedback control portion and apseudo control portion. The feedback controls, depicted on the left side of the figure, combine signalsfrom the pilot controls and the airplane sensors to calculate the airplane accelerations required forstability in flight and response to piloting commands. The feedback gains are calculated using theCRAFT methodology reported in reference 14. This process uses Direct Eigenspace Assignment to makethe airplane’s stability characteristics have level 1 (satisfactory) flying qualities where possible. Lateralcontrol stick gains are scheduled to achieve the roll rates specified by the design guidelines reported inreference 12. Rudder pedal gains are scheduled to achieve 10 degrees of sideslip angle. Lateral controlstick and rudder pedal signals are cross-fed to minimize the angle of sideslip during rolling maneuvers.

11

AeroControls

ThrustVectoring

InertialCoupling

Inter-connect

Dis- trib- utor

NormalizedBody-Axis

Control Moments

Gains

VaneReliefSensors

Feedback Controls Pseudo Controls

Stability-AxisAngular

Accelerations

EngageStrakeEngage

StrakeControl

ForebodyStrakes

VectorEngage Engage

ControlStick

RudderPedals

vlat

vdir

vroll

vyaw

Figure 5. Lateral/Directional Control System Overview.

The pseudo controls portion, the subject of this report, positions the conventional aerodynamic controlsurfaces (aileron, rudders, and differential stabilators), the thrust-vectoring mechanisms, and the actuatedforebody strakes in response to the acceleration commands generated from pilot command and sensorfeedbacks. The stability-axis roll acceleration is vla t , rad/sec2, and the stability-axis yaw acceleration isvdir, rad/sec2. The amounts of body-axis roll and yaw control moments needed to produce theseaccelerations are calculated, including moments needed to counter inertial coupling effects. Calculationsare made of the available control moments from the conventional controls, the thrust-vector controls, andthe actuated forebody strakes. The ratios of the required moments to the available moments become thepseudo control variables vroll and vyaw. These are used to drive the aerodynamic controls according toschedules that decouple roll and yaw moments. Some of the control moments may be produced by thethrust-vectoring controls and the actuated forebody strakes. A vane relief function is used to transferslow, steady deflections from the thrust-vectoring controls to the aerodynamic controls. A more detaileddevelopment of the pseudo controls portion of the control law is given in the following sections.

Controls Interconnect

This section describes the transformation of lateral/directional angular acceleration commands into rolland yaw pseudo control variables. The lateral acceleration command, vlat, is an instantaneous angularacceleration command about the stability x-axis that causes rolling motions, generally about the velocityvector. The directional acceleration command, vdir is an instantaneous angular acceleration about thestability z-axis that causes yawing motions perpendicular to the velocity vector to produce sideslip.These commands are generated from combinations of pilot commands and sensor feedbacks. Thecontrols interconnect transforms the acceleration commands into body-axis pseudo control variables thatare then distributed to the individual control effectors as described in a following section. Theinterconnect includes compensation for inertial coupling effects.

12

Axis Transformation

The commands from the feedback controls to pseudo controls are the lateral pseudo control variable,vlat, and the directional pseudo control variable, vdir. The lateral pseudo control variable commands aninstantaneous angular acceleration about the velocity vector that is a combined rolling and yawingacceleration about the airplane body axes as is shown in figure 6a. The directional pseudo controlvariable commands an instantaneous acceleration about an axis that is perpendicular to the velocity vectoras is shown in figure 6b. The lateral and directional pseudo control variables are combined in thefollowing axis-transformation formulas (1) to produce the body-axis acceleration commands.

˙

˙cos sin

sin cos

p

r

v

vcmd

cmd

lat

dir

=

( ) − ( )( ) ( )

α αα α

(1)

V

α

rcmd

– pcmd

rs = vdir

V

α

ps = vlat

pcmd

rcmd

a) Lateral Command, vlat. b) Directional Command, vdir.

Figure 6. Stability-Axis Commands.

Moment Commands

The moments required to produce the desired roll and yaw accelerations are functions of the inertialcharacteristics of the airplane and the desired accelerations. Gyroscopic coupling also causesaccelerations during airplane rotational motions. Additional moments required to cancel this inertialcoupling are calculated as functions of the inertial characteristics and the angular body-axis rates of theairplane.

L

N

I I

I I

p

r

I I I

I I I

p q

r qcmd

cmd

XX XZ

XZ ZZ

cmd

cmd

XZ ZZ YY

YY XX XZ

=

−−

+

− −− +

( )( )

˙

˙(2)

The first term on the right-hand side of equation (2) translates the desired angular accelerations into therequired body-axis moments and the second term compensates for inertial coupling.

Pseudo Control Variables

The above development yields the roll and yaw moments required for the airplane to respond to thestability-axis acceleration commands and to offset the effects of inertial coupling. The required moments

13

are divided by the available moments to yield pseudo control variables that indicate the fraction of theavailable moments needed. The roll pseudo control variable, vroll, is the fraction of the available body-axis roll moment and the yaw pseudo control variable, vyaw, is the fraction of the available body-axis yawmoment.

Roll control moments are generated by coordinated deflections of the conventional aerodynamiccontrols (ailerons, rudders, and differential motions of the horizontal stabilators) and may besupplemented with roll control moments generated by the thrust-vectoring system. Similarly, yaw controlmoments are generated by coordinated deflections of the conventional aerodynamic controls and may besupplemented with yaw control moments generated by the thrust-vectoring system and by differentialdeflections of the ANSER (actuated forebody strakes) controls.

Generation of yaw control moments by the thrust-vectoring system also causes rolling momentsbecause the center of gravity of the airplane is displaced vertically from the line of thrust of the engines.This displacement is a vertical moment-arm on which the yaw-vectoring forces act, resulting in rollingmoments. The ratio of the rolling moments to the yawing moments caused by yawing-momentcommands equals the ratio of the vertical moment arm, lz, to the distance that the thrust-vectoringapparatus is aft of the center of gravity, lTV. The rolling moments are compensated by cross-feeding aportion of the yawing moment command into the rolling moment command.

v N Nyaw cmd avail= (3)

v Ll

lN v Lroll cmd

z

TVTV yaw avail= −

(4)

Roll Acceleration

The roll acceleration capability of the airplane about its stability axis is calculated. This value isprovided for use in scheduling lateral (roll) commands derived from lateral motions of the control stick(see reference 11). Equations (5)–(7) are used to calculate this value. Figure 7 depicts the geometry uponwhich the equations are based.

˙ ˙ cos ˙ sin,max max maxp p rs = + α α (5)

where

˙ maxpL

Iavail

XX= (6)

rmax = NavailIZZ (7)

The calculated stability-axis roll acceleration capability is the sum of the contributions of the body-axis roll and yaw acceleration capabilities. The body-axis accelerations are calculated from the availableroll and yaw moments and the body-axis moments of inertia. The effects of the cross product of inertia,IXZ, are ignored. The calculations do not account for the balance between the roll and yaw axis controlsrequired for coordination.

14

V

α

pmax

rmax

ps, max

Figure 7. Maximum Stability-Axis Roll Acceleration.

Controls Distribution

This section describes the distribution of roll and yaw control commands to the conventional airplanelateral/directional flight controls (ailerons, rudders, and differential stabilators), the thrust-vectoringsystem, and to the actuated forebody strake controls. The controls are coordinated to provide a rollcommand channel and a yaw command channel. Commands to the roll command channel causecoordinated control deflections that produce body-axis roll moments with minimal yawing moments andcommands to the yaw command channel produce body-axis yaw moments with minimal rollingmoments. Side forces are not considered as an independent control influence in this development becausethey are closely related to the yaw control moments.

Distribution of Conventional Controls

The three conventional controls used for lateral and directional control are: (1) ailerons that aredeflected differentially, (2) twin rudders that are deflected collectively, and (3) stabilators that aredeflected differentially. These controls produce varying amounts of rolling moment, yawing moment,and side force depending on flight condition, especially dynamic pressure, angle of attack, and symmetricstabilator position. The object of the following development is to determine schedules for coordinatingthe conventional controls so that (1) rolling commands cause body-axis rolling moments with aminimum of yawing moment and (2) yawing commands cause body-axis yawing moments withminimum rolling moments. Additional schedules are determined that predict the rolling and yawingmoments that can be generated by the conventional controls when operating according to the distributionschedules.

Control Moments – Conventional Controls

The roll and yaw moments generated by deflection of the conventional aerodynamic controls are givenin equations (8) and (9).

L q S b C C Cl a a l r r l d d= + +( ) δ δ δδ δ δ (8)

N q S b C C Cn a a n r r n d d= + +( ) δ δ δδ δ δ (9)

15

The roll and yaw control coefficients are primarily functions of angle of attack and examples are givenin figures 8 and 9. These figures depict the rolling and yawing moments produced by each of theconventional controls when deflected to its limit. These data were derived from a HARV simulationmodel (references 15 and 16) having the leading- and trailing-edge flaps in the clean configuration.

-0.01

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

-10 0 10 20 30 40 50 60 70 80 90

∆Clδa∆Clδd∆Clδr

∆Cl

AOA, degrees

Figure 8. Example Roll Control Moment Coefficients of Conventional Controls, Mach 0.2, altitude 30 000 ft,stabilator –6.75 deg.

-0.12

-0.10

-0.08

-0.06

-0.04

-0.02

0.00

0.02

-10 0 10 20 30 40 50 60 70 80 90

∆Cnδa∆Cnδd∆Cnδr

∆Cn

AOA, degrees

Figure 9. Example Yaw Control Moment Coefficients of Conventional Controls, Mach 0.2, altitude 30 000 ft,stabilator –6.75 deg.

16

Distribution Schedule Calculations

Let u→

be a vector containing the deflections of each of the conventional controls normalized by its

maximum value. Let croll →

be a vector containing the roll moment coefficients that result from maximum

deflection of each conventional control. Let cyaw →

be a vector containing the yaw moment coefficientsresulting from maximum deflection of each conventional control.

ua am

r rm

d dm

→=

δ δδ δδ δ

(10)

c

C

C

Croll

l a

l r

l d

→=

∆∆∆

δ

δ

δ

(11)

c

C

C

Cyaw

n a

n r

n d

→=

∆∆∆

δ

δ

δ

(12)

The roll and yaw control coefficients for deflections of the conventional controls are calculated as thescalar products of equations (10) and (11), and of equations (10) and (12), respectively.

C c uroll roll

T

= → →

(13)

C c uyaw yaw

T

= → →

(14)

Let the normalized control deflections be specified by linear combinations of two control distributionvectors as follows.

u d v d vroll roll yaw yaw→ → →

= + (15)

where vroll and vyaw are pseudo control variables for roll and yaw control moments, respectively,

and where droll →

and dyaw →

are the corresponding distribution vectors. Distribution vectors are desired

such that the distribution vector for roll control, droll →

, causes maximum rolling moment with a minimum

yawing moment while the distribution vector for yaw control, dyaw →

, causes a maximum yawing momentwith a minimum rolling moment. The roll distribution vector is the solution of the following optimizationproblem:

17

Find d droll→ →

= to maximize

J d c c d d c c dT

roll roll

T T

yaw yaw

T

= −→ → → → → → → →

(16)

where

d dT→ →

= (constant)2 (17)

The roll distribution vector, droll →

, is the eigenvector corresponding to the positive eigenvalue of thesymmetric matrix W where

W c c c croll roll

T

yaw yaw

T

= → → → →

− (18)

Conversely, the yaw distribution vector minimizes equation 16 subject to the constraint of equation 17.

The yaw distribution vector, dyaw →

, is the eigenvector corresponding to the negative eigenvalue of matrixW. The third eigenvector of matrix W corresponds to a zero eigenvalue. This eigenvector lies in acontrol subspace that has no effect on the roll and yaw control moments and represents contradictorycontrol deflections that cancel each other. Since the third eigenvector is not used by equation 15 ingenerating control deflections, contradictory control deflections are eliminated.

The pseudo control variables, vroll and vyaw, are dimensionless and range between –1.0 and +1.0 (see

equation 15). The distribution vectors, droll →

and dyaw →

, are normalized to make their maximum elements

unity. Distribution vector, droll →

, contains the deflections of the conventional controls, normalized bytheir maximum values, that produce the maximum body-axis rolling moment within the capabilities of the

controls. Likewise, distribution vector, dyaw →

, contains the normalized deflections of the controls thatproduce the maximum yawing moment.

Distribution Schedules

Several sets of data for the roll and yaw control coefficients as depicted in figures 8 and 9 wereobtained. The data were taken for Mach numbers of 0.2, 0.4, 0.6, and 0.8; altitudes of 10 000 ft,30 000 ft, and 50 000 ft; and symmetric tail deflections of –24.0 degrees (hard-over TEU),–15.375 degrees, –6.75 degrees (mid-range), +1.875 degrees, and +10.5 degrees (hard-over TED). Theauthority of the differential tail varies according to the symmetric tail position. The amount of freemotion available for differential tail commands ranges from a maximum of ±17.25 degrees when thesymmetric tail position is at the center of its range of travel to a minimum of zero when the symmetric tailposition is hard-over in either direction.

Distribution schedules were calculated for each data set. The distribution schedules were averagedtogether and piecewise linear functions were fitted. The averaging was weighted to favor the trailing-edge-up data for large, post-stall angles of attack (≥ 44 degrees). The resultant distribution schedules for

18

roll and yaw control are presented in figures 10 and 11 with the normalization removed. The schedulesfor differential tail deflections are given for the symmetric tail at its mid-range value,–6.75 degrees, where the differential tail has the maximum authority of ±17.25 degrees. For othersymmetric tail angles, the differential tail schedules must be reduced in proportion with the reduction indifferential tail authority.

-30

-20

-10

0

10

20

30

-10 0 10 20 30 40 50 60 70 80 90

Controls,degrees

AOA, degrees

Aileron (±25°)

Rudder (±30°)

Diff Stab (±17.25°)

Diff Stab ScheduleModified According toPitch Stab Command

PseudoControls

vroll = 1.0vyaw = 0.0

Figure 10. Roll Control Distribution Schedules.

-40

-30

-20

-10

0

10

20

30

-10 0 10 20 30 40 50 60 70 80 90

Controls,degrees

AOA, degrees

Aileron (±25°)

Rudder (±30°)

Diff Stab (±17.25°)

Diff Stab ScheduleModified According toPitch Stab Command

PseudoControls

vroll = 0.0vyaw = 1.0

Figure 11. Yaw Control Distribution Schedules.

Conventional Controls Coefficients

In order to coordinate the lateral and directional axes of the airplane during flight through widelyvarying conditions with the possibility of engaging thrust-vectoring controls and actuated forebodystrakes, it is necessary to calculate the roll and yaw control moments available from the different controls.

19

For the conventional controls, it is assumed that the above distribution schedules are effective indecoupling the roll and yaw axes. That is, the roll pseudo control variable, vroll , causes body-axis rollmoments while any yaw moments can be neglected. Similarly, the yaw pseudo control variable, vyaw,causes body-axis yaw moments with negligible roll moments.

The roll coefficient produced by a unit of the roll pseudo control variable, vroll, is calculated by com-bining equations (13) and (15) with the yaw pseudo control variable, vyaw, set to zero (equation 19).Similarly, the yaw coefficient produced by a unit of the yaw pseudo controls variable is calculated bycombining equations (14) and (15) with the roll pseudo control variable set to zero (equation 20).

C

vc droll

roll vroll

T

roll

yaw =

→ →=

0

(19)

C

vc d

yaw

yaw v

yaw

T

yaw

roll =

→ →=

0

(20)

These coefficients were calculated using the above distribution schedules for droll →

and dyaw →

. The re-sults were fitted with piecewise linear functions of angle of attack, differential tail authority, altitude, andMach number. The roll and yaw controls coefficients corresponding to unity values of the roll and yawpseudo control variables are plotted in figures 12 and 13, respectively, for 30 000 ft altitude and 0.2 Machnumber.

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

-10 0 10 20 30 40 50 60 70 80 90

Croll

AOA, degrees

Roll Moment = Croll q S b

Mach 0.2, 10 kft ≤ alt ≤ 50 kft, Stab CenteredVaries with Mach, Altitude, Pitch Stab Command

Aerodynamic Controls Only

PseudoControl

vroll = 1.0vyaw = 0.0

Figure 12. Total Available Roll Control Coefficient for Conventional Controls.

20

0.00

0.01

0.02

0.03

0.04

0.05

0.06

-10 0 10 20 30 40 50 60 70 80 90

Cyaw

AOA, degrees

Yaw Moment = Cyaw q S b

Stab Hard-Over

Mach 0.2, 10 kft ≤ alt ≤ 50 kftVaries with Mach, AltitudeAerodynamic Controls Only

PseudoControl

vyaw = 1.0vroll = 0.0

–14.0 ≤ Stab ≤ +0.5

Figure 13. Total Available Yaw Control Coefficient for Conventional Controls.

The amount of rolling and yawing control moments that can be generated by the conventional controlsare calculated by combining the coefficients with dynamic pressure.

L q S b Caero roll= (21)

N q S b Caero yaw= (22)

Distribution of Thrust-Vectoring Controls

The thrust-vectoring apparatus is designed to generate pitch, roll, and yaw control moments bydeflecting the exhaust of the engines vertically and horizontally. Symmetric vertical deflections causepitching moments, differential vertical deflections cause rolling moments, and horizontal deflectionscause yawing moments. The roll and yaw thrust-vector angles are commanded in proportion to the rolland yaw pseudo control variables, respectively.

δ δTVr TVrm rollv= + (23)

δ δTVy TVym yawv= − (24)

The thrust-vectoring control moments are proportional to the deflection angles and the thrust of theengines. The following equations describe the body-axis roll and yaw moments produced by the roll andyaw thrust-vectoring controls.

L L vl

lN vTV roll

z

TVTV yaw= − (25)

N N vTV yaw= (26)

21

The rolling moment capability of the rolling thrust-vector controls is a function of the maximum rollingthrust-vector angle, total engine thrust, and the lateral position of the engines.

L l TTV y TVrm=

πδ

180(27)

The yawing moment capability of the yawing thrust-vector controls is a function of the maximum yawingthrust-vector angle, total engine thrust, and the longitudinal distance between the thrust-vectoring nozzlesand the airplane center of gravity.

N l TTV TV TVym=

πδ

180(28)

Distribution of Actuated Forebody Strake Controls

The actuated forebody strakes are mounted in a specially built radome. Each strake is actuatedindependently from a closed position (0 degrees) to a fully deployed position (90 degrees). These devicescontrol the flow separation and vortices about the forward part of the airplane that induce moments thatcan be used for flight control. Wind tunnel studies have shown that actuated forebody strakes generateusable yawing control moments at elevated angles of attack (references 9 and 10). Rolling moments,however, are generally small. Therefore, for the design of the ANSER control system, the actuatedforebody strakes are considered to be purely producers of yawing control moments.

Actuated Forebody Strake Dead-Band

During development of the ANSER control concept (reference 9), it was found that at higher angles ofattack, deflecting one strake at a time could result in an undesirable control deadband or reversal for smallstrake deflections. When using the strake deflection schedule shown in figure 14a, positive differentialstrake commands, intended to generate negative (nose to the left) moments, produced deflections of theright strake with the left strake remaining at zero deflection (flush with the forebody). Similarly, negativedifferential commands caused deflections of only the left strake. However, it was found that the strakesmust be commanded to a significant angle before yawing moments are produced in the desired direction,

90

60

30

0

+90+60+300–90 –60 –30

b) 30 degrees Symmetric Deflection.

Differential Strake Command, degrees

Right StrakeLeft Strake

90

60

30

0

+90+60+300–90 –60 –30

a) No Symmetric Deflection.

StrakeAngle,degrees

Differential Strake Command, degrees

Right StrakeLeft Strake

Figure 14. Actuated Forebody Strake Deflections versus Differential Strake Command.

22

especially at higher angles of attack. This leads to an objectionable deadband about the neutral commandcondition. A typical relationship between differential strake deflection and yawing moment is depicted asthe solid line in figure 15. The deadband characteristic occurs above 30 degrees angle of attack and ismost pronounced above 60 degrees.

The deadband characteristic was eliminated by incorporating a symmetric deployment schedule to theactuated forebody strake position commands. The schedule is a function of angle of attack and causes thestrakes to deploy symmetrically when the angle of attack is large and the differential command is small.An example of the strake deflections versus differential command incorporating a symmetric deploymentis shown in figure 14b. At zero differential command, both strakes are deflected to the requiredsymmetric deployment angle. Differential control commands cause one strake to deflect further and theother to retract in unison until it becomes flush with the forebody. For larger differential commands, thestrakes revert to the original schedule of figure 14a. The largest magnitude command (±90 degrees)results in one strake being fully deployed and the other being fully retracted. The symmetric deploymentschedule ‘linearizes’ the control moment for small differential commands as depicted by the dashed lineon figure 15.

Differential Strake Deflection, degrees

Yaw Moment

–60–90 –30 0 +30 +60 +90

Right Strake

Left Strake with Symmetric Schedule

Deadband

Figure 15. Actuated Forebody Strake Control Moments with and without Symmetric Strake Schedule.

Actuated Forebody Strake Calibration

Another nonlinearity of the yawing moment generated by the actuated forebody strakes is a variationof the incremental effectiveness depending on the amount of differential strake deflection. This is seenon figure 16 as a large reduction in the slope (by a factor of 2.75) at large differential deflection angles(solid line). This nonlinearity is corrected by driving the differential strakes by a nonlinear function ofthe yaw pseudo controls, vyaw.

δFS yaw yawv v= − +( )48 1 0 875 2 . (29)

The term in the parentheses acts as a variable gain that reduces the slope of the yaw moment curve forsmall commands. The effect of the correction is shown by the dashed line in figure 16.

23

Yaw Moment, Cn

–1.0 0 +1.0

with Symmetric Schedule

with Calibration

Yaw Pseudo Control Variable, vyaw , no unit

Figure 16. Actuated Forebody Strake Control Moment with and without Calibration.

The yawing control moment produced by full differential deflection of the actuated forebody strakes isa function of angle of attack depicted in figure 17. The yawing control moment that can be generated bythe actuated forebody strakes is calculated by combining the control coefficient with dynamic pressure.

N q S b CFS n FS= ∆ , (30)

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

0 10 20 30 40 50 60 70 80AOA, degrees

∆Cn , F S

Figure 17. Available Actuated Forebody Strake Yaw Control Moment.

24

Controls Coordination

The controls distribution section has discussed the distribution of the roll and yaw pseudo controlsvariables, vroll and vyaw, to the conventional aerodynamic controls, equation (15), to the thrust-vectoringcontrols, equations (23) and (24), and to the actuated forebody strakes, equation (29). The range of eachpseudo control variable is ±1.0 and it commands a specified fraction of the amount control moment forits axis of control. If vyaw equals 0.2, for example, the conventional controls deflect to produce 20 per-cent of their yaw moment capability, the yaw thrust-vectoring apparatus deflects 20 percent, and theactuated forebody strakes deflect 20 percent. Operating in this manner, the different controls reach theirlimits as the pseudo control variable reaches unity magnitude.

Combining the roll and yaw moments produced by the conventional aerodynamic controls(equations 21 and 22), the thrust-vectoring controls (equations 25 and 26), and the actuated forebodystrakes (equation 30), yields the body-axis roll and yaw moments as functions of the roll and yaw pseudocontrol variables.

L q S b C L vl

lN vroll TV roll

z

TVTV yaw= +[ ] − (31)

N q S b C N q S b C vyaw TV n FS yaw= + +[ ] ∆ , (32)

The controls distribution method discussed above converts the task of calculating command deflections ofseveral control effectors (six in this case: ailerons, rudders, differential horizontal stabilizer, roll and yawthrust vectoring controls, and differential forebody strakes) into one of specifying two pseudo controlvariables, one each for the roll and yaw airplane axes.

Accelerometer Correction

The lateral accelerometer in the original airplane design was located to minimize interference by theforces produced by the rudder. Rudder forces cause a linear acceleration and a rotational acceleration thatcombine to cause the airplane to initially rotate about a point forward of the center of gravity. Placementof the accelerometer at this point eliminates a direct coupling of the rudder forces to the accelerometeroutput that can interfere with control system operation. However, since the experimental thrust-vectoringsystem and the actuated forebody strakes are at different locations on the airplane, forces produced bythem cause rotations about points that may be some distance from the accelerometer. Estimates of theinterference terms are calculated in the control law and they are used to correct the accelerometer signal.

Figure 18 depicts a notional plan view of the airplane showing the placement of the thrust-vectoringsystem, the actuated forebody strakes, and the lateral accelerometer. The thrust-vectoring systemgenerates forces, FTV, concentrated at a distance, lTV, aft of the c.g. The actuated forebody strakesgenerate forces, FFS, concentrated at a distance, lFS, forward of the c.g. Aerodynamic forces, Faero, andmoments, Naero, that result in the usual accelerations at the sensor, are considered to act at the center ofgravity. The lateral accelerometer is located at a distance, la, forward of the c.g.

The lateral acceleration of the center of gravity and the rotational acceleration are given by thefollowing approximations:

25

aF F F

mcgaero TV FS= + +

(33)

rN l F l F

Iaero TV TV FS FS

ZZ= − +

(34)

These equations are combined to yield the lateral acceleration at the sensor location.

aF

ml

N

I

l

I

l

l mN

l

I

l

l mNy

aeroa

aero

ZZ

a

ZZ TVTV

a

ZZ FSFS= +

+ −

+ +

(35)

where

N l FTV TV TV= − (36)

N l FFS FS FS= (37)

ForebodyStrakes

Center ofGravity

LateralAccelerometer

Thrust-VectorControls

lTV

ay

FFS

la

lFS

FTV

FaeroNaero

ly

Figure 18. Plan view of Airplane Showing Lateral Accelerometer Interference.

The first term of equation (35) is the usual lateral acceleration at the sensor location and includes theeffects of rudder control forces. The next two terms are interference caused by thrust-vectoring andactuated forebody strake forces, respectively. These terms may cause instantaneous response in thesensor signal to control commands that result in objectionable oscillations. They can also cause constantoffsets of the sensor signal during steady maneuvers that can affect airplane performance. A correctionfor the accelerometer may be calculated using the interference terms of equation (35).

a a N a N vy corr y corr TV y corr FS yaw, , ,= +[ ] (38)

26

where

al

I

l

l my TVa

ZZ TV, = −

(38a)

al

I

l

l my FSa

ZZ FS, = −

(38b)

The calculation of the interference of thrust vectoring on the accelerometer (equation 38a) is obtainedusing airplane mass and dimensional data.

In order to calculate the interference of the actuated forebody strakes on the accelerometer (equation38b), the ratio of the moment to force produced by differential strake deflections was calculated at eachpoint in the database to obtain an effective moment arm, lFS. An average value for the moment arm ateach angle of attack was used. A schedule of the interference acceleration caused by actuated strakecontrol moments as a function of angle of attack is presented in figure 19. The calculated data are shownas symbols and the schedule is shown as a line.

9.0 10-5

1.0 10-4

1.1 10-4

1.2 10-4

1.3 10-4

1.4 10-4

10 20 30 40 50 60 70 80

dataschedule

ay,FS

ft/sec2 perft-lb

AOA, degrees

Figure 19. Lateral Accelerometer Correction for Actuated Forebody Strakes.

Thrust-Vectoring Engagement

This section describes the schedules that engage the yaw and roll thrust-vectoring controls as functionsof flight condition and engine thrust level. The thrust-vectoring controls are regulated by schedulingvariables STVy for the yaw axis and STVr for the roll axis. For each axis, the thrust-vectoring controls areengaged or ‘on’ when the scheduling variable is unity and are disengaged or ‘off’ when it is zero.Intermediate values of the scheduling variable cause partial engagement of the respecting thrust-vectoringcontrol. The scheduling variables are used as multiplying gains on the thrust-vectoring commands.Equations (23) and (24) are rewritten to include the scheduling variables

δ δTVr TVm TVr rollS v= (39)

27

δ δTVy TVym TVy yawS v= − (40)

The moment capabilities of the thrust-vectoring controls vary with the scheduling variables. Equations(27) and (28) are rewritten to include the scheduling variables

L l T STV y TVrm TVr=

π δ180

(41)

N l T STV TV TVym TVy=

π δ180

(42)

The accounting of the scheduled thrust-vectoring moments in the total available rolling and yawingcontrol moments, Lavail and Navail, used in equations (3) and (4) makes the rolling and yawing momentsinsensitive to the value of the schedule variables. For example, if thrust vectoring is turned on for eitheraxis at some point in flight, the increased available control moment is accounted for by a reduction in thecorresponding pseudo control variable. The subsequent reduction in the control moment produced by theaerodynamic controls is balanced by the control moment introduced by the thrust-vectoring control(assuming none of the controls is saturated). Within the accuracy of the design calculations, the airplane'sflight behavior is unaffected when the thrust-vectoring controls are turned on or off. Therefore, thefeedback gains used in a control system do not need to be adjusted and feedback loops do not need to beadded to the control system to account for the presence of thrust-vectoring controls. However, commandgains may be increased when thrust-vectoring controls are engaged to take advantage of the increasedcontrol power.

Thrust-Vectoring Schedules

The scheduling variables are determined using calculated values of the control moments availablefrom the aerodynamic controls (including actuated forebody strakes, if used) and the control momentsavailable from the thrust-vectoring controls. These moments are given by equations (21), (22), (27), and(28). The schedules cause the thrust-vectoring controls to be disengaged (scheduling variable = 0) whenthe aerodynamic controls are at least twice as powerful as the thrust-vectoring controls. Thrust-vectoringcontrols are fully engaged (schedule variable = 1) when they are at least as powerful as the aerodynamiccontrols.

S

N N

N

NN N N

N N

TVy

TV aero

aero

TVaero TV aero

TV aero

=

<

− ≤ ≤

>

01

2

21

21

,

,

,

(43)

S

L L

L

LL L L

L L

TVr

TV aero

aero

TVaero TV aero

TV aero

=

<

− ≤ ≤

>

01

2

21

21

,

,

,

(44)

28

Figure 20 depicts the yaw control moments produced by the aerodynamic controls and yaw thrust-vectoring controls as functions of dynamic pressure. Figure 20a depicts the aerodynamic and thrust-vectoring control moments individually. The aerodynamic control moment is proportional to dynamicpressure with a coefficient, Cyaw, of 0.04. This coefficient is representative of the yaw control capabilityof the HARV conventional controls at low angles of attack (see figures 9 and 13). The bold lines onfigure 20a depict the yaw thrust-vectoring capability of the HARV for two thrust levels approximatelyequal to full- and half-thrust at test altitude. The yaw thrust-vectoring moments are calculated fromequations 42 and 43. Figure 20b depicts the yaw control moment produced by the combination of theaerodynamic and thrust-vectoring controls. Line 0-➀ on the figure (from the origin to the point markedas ➀) is the yaw moment produced by the aerodynamic controls only (also shown on figure 20a).Line 0-➁ is twice this yaw moment. The bold, solid line ➂-➃-➄-➀ is the total yaw control moment whenthrust is 15 000 lb. For higher airspeeds, dynamic pressure is large and yaw thrust vectoring is off.

0

40,000

80,000

120,000

160,000

0 50 100 150 200 250

AerodynamicT = 15 000 lbT = 7 500 lb

N, ft-lb

Transition

Dynamic Pressure, lb/ft2

STVy = 1

(yaw TV on)

STVy = 0

(yaw TV off)

a) Individual Aerodynamic and Thrust-Vectoring Yaw Control Moments.

0

40,000

80,000

120,000

160,000

200,000

0 50 100 150 200 250

T = 15 000 lbT = 7 500 lb

N, ft-lb

Transition

Dynamic Pressure, lb/ft2

➀

➁

STVy = 1

(yaw TV on)

STVy = 0

(yaw TV off)

➂

➃➄

b) Combined Aerodynamic and Thrust-Vectoring Yaw Control Moments.

Figure 20. Yaw Thrust-Vector Schedules for Cyaw = 0.04.

29

Under these conditions, the yaw moment is given by the line segment ➀-➄. This corresponds to the firstterm of equation (43). In the transition region, the moment produced by the aerodynamic controls isbetween one and two times that available from the thrust-vectoring controls. The thrust-vectoringcontrols are scheduled on with decreasing dynamic pressure to maintain total control moment at aconstant value equal to twice that available from the thrust-vectoring controls shown as line segment➃-➄. This corresponds to the second term of equation (43). For low values of dynamic pressure, thethrust-vectoring controls are fully on and the yaw moment equals that of the aerodynamic controls plusthat of the thrust-vectoring controls, depicted as line segment ➂-➃. This corresponds to the third term ofequation (43). The effect of reducing thrust is depicted on figure 20b by the bold, dashed line. Since theyaw thrust-vectoring capability is reduced, the switch points, ➃ and ➄, are shifted to lower values ofdynamic pressure.

Figure 21 depicts the roll control moment produced by the combination of the aerodynamic and thrust-vectoring controls. The aerodynamic control moment is proportional to dynamic pressure with acoefficient, Croll, of 0.07. This coefficient is representative of the roll control capability of the HARVconventional controls at low angles of attack (see figures 8 and 12). Roll thrust-vectoring control can beused over a much smaller range of dynamic pressure than the yaw control because the close spacing ofthe engines results in a relatively weak roll moment producing capability.

0

5,000

10,000

15,000

20,000

25,000

0 5 10 15 20

T = 15 000 lbT = 7 500 lb

L, ft-lb

Transition

Dynamic Pressure, lb/ft2

STVr = 1

(roll TV on)

STVr = 0

(roll TV off)

Figure 21. Roll Thrust-Vectoring Schedules for Croll = 0.07.

Thrust-Vectoring Envelopes

Figures 22–24 illustrate the thrust-vectoring envelopes that result from using the schedules ofequations (43) and (44). A number of points indicating level, nonaccelerating, 1g flight conditions areincluded on the figures for reference. Each figure shows boundaries between the thrust-vectoring-offregion, the transition region, and the thrust-vectoring-on region. These are plotted against equivalentairspeed (KEAS) for a range of angle of attack. The boundaries are given for flight at 25 000 feet altitudeusing aerodynamic data for Mach 0.2 and a nominal thrust level of 15 000 pounds. On the boundariesbetween the thrust-vectoring-off and transition regions, the aerodynamic control moments are double thethrust-vectoring control moments. On the boundaries between the transition and the thrust-vectoring-onregions, the aerodynamic control moments equal the thrust-vectoring control moments. Changes in theboundary locations caused by varying aerodynamic control derivatives with altitude and Mach number

30

are relatively small and are not shown. Two sets of boundaries are plotted on each figure. The solid linesindicate boundaries for conditions where the stabilators are commanded hard-over to their travel limits bylarge longitudinal control commands preventing their use in producing rolling or yawing moments. Thedashed lines indicate the boundaries when the stabilators are free to move ±10 degrees differentially. Theyaw and roll moments available from differential stabilator deflections cause the boundaries to shift toslower airspeeds. The boundary locations are sensitive to changes in thrust caused by altitude changes,speed changes, and throttle position. Increases in thrust cause the boundaries to shift to higher airspeeds(upwards on the figures) and decreases in thrust cause shifts to lower airspeeds. The shifts follow asquare root relationship with thrust such that a doubling of thrust causes the airspeeds to increase by afactor of the square root of two.

Figure 22 presents the yaw thrust-vectoring envelopes when the actuated forebody strakes are notused. For low angles of attack (less than 16 degrees), the yaw thrust-vectoring controls are off whenairspeed is greater than 240 KEAS, and they are on when airspeed is less than 170 KEAS, with atransition between these airspeeds. For angles of attack between 16 and 28 degrees, the yaw controlmoment coefficient for the conventional controls decreases (see figure 13). Dynamic pressure must beincreased in order to have the same control moments as at the lower angles of attack. Therefore, theboundaries shift to higher airspeeds for angles of attack between 16 and 28 degrees. The yaw controlcoefficient for the aileron-rudder combination is constant for angles of attack greater than 28 degrees.This results in the boundaries being at constant airspeeds for hard-over collective deflections of thestabilators (solid lines). When the stabilators are free to move differentially, they are effective ingenerating yaw moments at angles of attack greater than 38 degrees. This causes the boundaries to be atmuch lower airspeeds (dashed lines). For trimmed, 1g flight at small angles of attack, the airspeed is highand the aerodynamic yaw control moment is at least twice the thrust-vectoring control moment. Yawthrust vectoring is off for these conditions. For large angles of attack, the airspeed is low and theaerodynamic moment is less than the thrust-vectoring moment. Yaw thrust vectoring is on for theseconditions. Figure 22 does not give a precise indication of the on-off state of the thrust-vectoring controlsfor the trimmed flight conditions shown because the boundaries are calculated for a nominal thrust of15 000 lb that is not necessarily the thrust for the trimmed conditions.

0

50

100

150

200

250

300

350

0 10 20 30 40 50 60 70 80 90

   Stabilator Hard-Over–14° ≤ Stabilator ≤ +0.5°  1-g Flight Conditions

KEAS

AOA, degrees

Yaw TV Off

Yaw TV On

Transit ion

Mach 0.2 dataAlt 25 000 ft

Thrust 15 000 lb

Figure 22. Yaw Thrust-Vectoring Envelopes without Actuated Forebody Strakes.

31

Figure 23 presents the yaw thrust-vectoring envelopes when the actuated forebody strakes are used.The figure is the same as figure 22 for angles of attack less than 19 degrees, because the forebody strakesproduce no yaw control moments here. For angles greater than 19 degrees, the strakes produce yawcontrol moments, especially near 50 degrees of angle of attack. This causes the boundaries to be at muchslower airspeeds than in figure 22 where strakes are not employed.

0

50

100

150

200

250

300

350

0 10 20 30 40 50 60 70 80 90

   Stabilator Hard-Over–14° ≤ Stabilator ≤ +0.5°  1-g Flight Conditions

KEAS

AOA, degrees

Yaw TV Off

Yaw TV On

Transition

Mach 0.2 dataAlt 25 000 ft

Thrust 15 000 lb

Figure 23. Yaw Thrust-Vectoring Envelopes with Actuated Forebody Strakes.

Figure 24 presents the roll thrust-vectoring envelopes. The figure shows roll thrust-vectoring controlsbeing turned on between the very slow airspeeds of 40 and 60 KEAS at low angles of attack because theyare very weak in comparison with the aerodynamic roll controls. The aerodynamic roll controlcoefficient is greatly diminished for large angles of attack (see figure 12). Therefore, the boundariesincrease to 110 and 160 KEAS at 60 degrees angle of attack. Roll thrust-vectoring controls are scheduledoff for 1g flight conditions at angles of attack less than 40 degrees and are scheduled on at 60 degrees.The boundaries are largely unaffected by the availability of differential stabilator controls (compare thesolid lines with the dashed lines).

Although the control system includes roll thrust vectoring in the design, this feature was not used inthe HARV flight test program because of interference from the priority limiting function ofMixer/Predictor program.

Vane Relief

Use of the thrust-vectoring vanes, unique for the HARV airplane, is restricted by heating constraints.In order to minimize vane heating, a ‘vane relief’ function was devised. This function transfers deflectioncommands from the thrust-vectoring controls to the aerodynamic controls to ‘wash-out’ the vanedeflections while maintaining the commanded control moments. Other thrust-vectoring mechanisms thatdo not have such heating constraints would not require the use of the vane relief function. This sectiondescribes functions included in the control distribution portion of the system to reduce long-termdeflections of the thrust-vectoring controls. The following discussion of the vane relief function can beapplied to each of the control axes with an appropriate substitution of symbols and subscripts.

32

0

50

100

150

200

250

300

350

0 10 20 30 40 50 60 70 80 90

   Stabilator Hard-Over–14° ≤ Stabilator ≤ +0.5°  1-g Flight Conditions

KEAS

AOA, degrees

Roll TV Off

Roll TV On

Transition

Mach 0.2 dataAlt 25 000 ft

Thrust 15 000 lb

Figure 24. Roll Thrust-Vectoring Envelopes.

General Design

Figure 25 depicts the routing of control moment commands to the aerodynamic and thrust-vectoringcontrols used in the developments of the previous sections. This circuitry does not include vane relief.

MA

MTV

+M

STV

vA

vTV

vCMC 1MA + STVMTV

Figure 25. Block Diagram of Aerodynamic and Thrust-Vectoring Control Moments.

For each axis, the control moments generated by the aerodynamic controls and the thrust-vectoringapparatus sum together.

M M v M vA A TV TV= + (45)

where

M Total control moment, ft-lb

MA Available aerodynamic control moment, ft-lb

MTV Available thrust-vectoring control moment, ft-lb

vA Aerodynamic pseudo control variable (full throw at ±1)

vTV Thrust-vectoring pseudo control variable

33

The previous sections have stated that the aerodynamic and thrust-vectoring controls are deflectedproportionally according to equations (46)–(48).

v vA C= (46)

v S vTV TV C= (47)

vM

M S MCC

A TV TV=

+ +(48)

where

MC Commanded control moment, ft-lb

STV Thrust-vectoring engagement control (0 - off, 1 - on)

vC Command pseudo control variable

The command pseudo control variable, vC, is the commanded control moment divided by the totalavailable control moment.

Figure 26 depicts the routing of control moment commands to the aerodynamic and thrust-vectoringcontrols including the vane relief circuitry (enclosed within the shaded boundary).

MMA

+

++

STV

vA

vTV

vC

1MA + STVMTV

MAMTV

MTVMA

+

+ +–

++

+

–+

MC

±1

MTV

+

++

vA,nom

vTV,nom

∆vA

±1 ∆vTV∆vA, filt

1Tcs + 1

Figure 26. Block Diagram of Vane Relief Circuit.

The vane relief circuitry calculates a steady adjustment for the aerodynamic control that is the lessor of(1) the amount of aerodynamic control that would be required to generate the control moment that isproduced by the thrust-vectoring control and (2) the amount of aerodynamic control that is available. Theadjustment is modified by a low-pass filter and is added to the aerodynamic control variable. The amountof thrust-vectoring control required to compensate for the aerodynamic control modification is calculated

34

and this is subtracted from the thrust-vector control variable. The thrust-vector control is ‘washed-out’ tozero for steady commands so long as the aerodynamic control is strong enough to satisfy the command.

The commanded control moment, MC, is divided by the total available control moment to produce thecommand pseudo control variable, vC. The total available control moment is the sum of the availableaerodynamic control moment, MA, the product of the available thrust-vectoring control moment, MTV,and the thrust vector engage variable, STV. The nominal aerodynamic pseudo control variable, vA,nom isset equal to vC, and the nominal thrust-vectoring pseudo control variable, vTV,nom is set equal to vCmultiplied by the engage variable, STV. This part of figure 26 is the same as figure 25.

The nominal thrust-vectoring pseudo control variable, vTV,nom is multiplied by the ratio of theavailable thrust-vectoring control moment to the available aerodynamic control moment, MTV/MA, tocalculate an equivalent amount of the aerodynamic pseudo control variable, vA. This is added to thenominal aerodynamic pseudo control variable, vA,nom, to calculate the aerodynamic control that would berequired to produce the commanded moment if there were no thrust vectoring control. The sum is limitedto ±1 to keep it within the available range of the aerodynamic control. The nominal aerodynamic pseudocontrol variable, vA,nom, is limited to unity and subtracted from this quantity to obtain the increment ofthe aerodynamic control, ∆vA, that can be commanded to alleviate the deflection of the thrust-vectoringcontrol.

The increment, ∆vA, passes through a low-pass filter to limit vane relief to steady and slowly varyingcommands. The output of the filter, ∆vA,filt, is added to the aerodynamic pseudo control variable, vA, totransfer the low-frequency part of the thrust-vectoring commands to the aerodynamic controls. Thissignal is also multiplied by the ratio of the aerodynamic control moment to the available thrust-vectoringcontrol moment, MA/MTV, to calculate a change of the thrust-vectoring control, ∆vTV, that is equivalentto the change made to the aerodynamic control. This change is subtracted from the nominal thrust-vectoring pseudo control variable, vTV,nom.

The moment, M, produced using the vane relief circuit is equal to the moment commanded, MC (solong as limiting does not occur elsewhere), and is independent of the output of the filter and theincrements being applied to the controls. When commanded moments are within the capability of theaerodynamic control alone, steady and slowly varying control actions are affected by the aerodynamiccontrol while rapidly changing and high frequency control actions are affected by both the aerodynamicand thrust-vectoring controls. The characteristics of the filter used in the circuit determine the divisionbetween low frequency and high frequency operation. For the first-order filter shown in the figure, the'crossover' frequency occurs at 1/Tc rad/sec. For a constant command, the thrust-vectoring control willseek its neutral condition so long as there is sufficient aerodynamic control power to satisfy the commandat a rate depending on the value of the time constant. When steady commanded moments exceed thecapability of the aerodynamic control alone, the aerodynamic control will seek its maximum value,vA = ±1, while the thrust-vectoring control will deflect away from its neutral position to make up thedeficit.

Figure 27 illustrates the operation of the vane relief logic for slowly varying and constant commands.The figure shows the moments generated by the aerodynamic and thrust-vectoring controls when the vanerelief filter is at a steady-state condition. Figure 27a shows a case where the aerodynamic controls aremore powerful than the thrust-vectoring control. In figure 27b, the thrust-vectoring control is strongerthan the aerodynamic controls. The figures show the moments generated by the aerodynamic controls,≤ MA, the thrust-vectoring control, ≤ MTV, and the total control moment, M, as functions of thecommanded moment, MC. Small commands, within the capability of the aerodynamic control alone, are

35

satisfied by the aerodynamic control with the thrust-vectoring control remaining at neutral. Largercommands result in maximum deflection of the aerodynamic controls with the thrust-vectoring controlsused to make up the difference.

M

MA

MTV

0

AeroThrust-Vector

Moments

0

1vTV

vA

MC

PseudoControls

M

MA

MTV

0

Aero

Thrust-Vector

Moments

0

1vTV

vA

MC

PseudoControls

a) MA > MTV . b) MTV > MA .

Figure 27. Steady-State Vane-Relief Moments versus Command Moment.

Filter Time Constant

The vane relief function, as described above, is not acceptable for two reasons. First, for smallmoment commands, the vane relief function operates as a linear washout-type function. Linear operationimplies that if the moment commands are small-amplitude sine waves, the outputs (surface deflectionsand thrust-vectoring commands) are sine waves also. Therefore, for sine wave commands, each thrust-vectoring vane is deflected into the engine exhaust jet 50 percent of the time. Since vane heating is afunction of whether the vanes are deflected into the jet or not (rather than on the amount of the deflectionsinto the jet), the vane relief function as described above fails to alleviate vane heating. Furthermore, ifthe moment command is a combination of a steady value with a rapidly varying sine wave superimposedupon it, the filter will move to a steady-state value according to the average value of the command and theaverage aerodynamic command and thrust-vectoring commands are adjusted as described above. Therapidly varying component is blocked by the filter and this component is passed to the aerodynamic andthrust-vectoring commands as in the previous figure. During periods of decreasing command magnitude,the aerodynamic and the thrust-vectoring controls may act in opposing directions. This is not acceptablebecause the aerodynamic and thrust-vectoring controls are in conflict. Both of these deficiencies arecorrected by manipulating the time constant of the filter.

For increasing moment commands, the output of the filter, ∆vA,filt, lags the input, ∆vA. The incrementsubtracted from the thrust-vectoring command, ∆vTV, is less than the nominal thrust-vectoring command,vTV,nom, resulting in incomplete cancellation. For such conditions the thrust-vectoring assists theaerodynamic controls so long as the command is increasing. The problem occurs when the command isbeing reduced. The lag of the filter causes the increment to be larger than the nominal thrust-vectoringcommand resulting in over-cancellation of the thrust-vectoring command. The aerodynamic commandsbecome larger than they need to be to generate the commanded moment and the thrust-vectoringcommands are in the opposite direction. In order to correct this operation, the filter is caused to quickly

36

bleed off as a function of its input and output values. The filter time constant varies according tofigure 28.

FilterInput

Filter Output

NormalTime Constant

FastTime ConstantTc = 0.125 sec

NormalTime ConstantTc = 1.25 sec

FastTime Constant

Figure 28. Variable Vane Relief Time Constant.

The filter operates with its normal time constant, Tc = 1.25 seconds, as long as the output is not greaterthan the input and the output has the same sign as the input . The region of normal operation is depictedas the wedge-shaped, clear areas on the figure. Should the operation of the filter leave this region, thefilter time constant is decreased to 0.125 second. This causes the output to rapidly transition towards thenormal operating region.

Simulation Example

Figure 29 presents time histories of the operation of the vane relief function. For this figure, themoment generating capabilities of the aerodynamic and thrust-vectoring controls are equal. Thecommanded moment (solid line on the top of the figure) is a sinusoidal function of varying frequencywith an amplitude that is within the capability of either control. Without the vane relief function, theaerodynamic control (dashed line) and the thrust-vectoring control (dotted line) would be equal to half ofthe command. With the vane relief function, the filter output, shown at the bottom of the figure, is usedto decrease the thrust-vectoring command with a compensating increase of the aerodynamic command toproduce the data shown at the top of the figure. The time constant of the filter is shown in the center ofthe figure.

For the first 7 seconds of the time histories, the vane relief function causes most of the requiredmoment to be generated by the aerodynamic control while reducing the thrust-vectoring contribution to arelatively small amount. The thrust-vectoring control is quickly reduced as the command decreases after6 seconds. This is characteristic of a linear washout filter. At 7 seconds, the thrust-vectoring controlreverses, becoming opposite in direction to the aerodynamic control. The time constant of the filter isreduced (to its fast value) to cause the filter to bleed rapidly so that the thrust-vector control remains nearneutral and the commanded moment is mainly produced by the aerodynamic control. At 8.6 seconds theaerodynamic and thrust-vectoring controls are in the same direction, each equals one half of thecommand, and the filter output crosses zero. The filter time constant reverts to its normal high value (itsslow value) and linear washout action resumes. As the frequency of the command increases, the vanerelief function allows larger commands to the thrust-vectoring controls as the relief action diminishes.

37

-1.00

-0.50

0.00

0.50

1.00

Total MomentAerodynamicThrust-Vectoring

NormalizedMoments,

ft-lb

0.00

1.50Filter TimeConstant,seconds

-0.50

0.00

0.50

0 2 4 6 8 10 12 14 16 18 20

FilterOutput

Time, seconds

Figure 29. Simulated Vane Relief Operation.

Concluding Remarks

A method for integrating aerodynamic and thrust-vectoring controls for the control of flight to highangles of attack has been presented. Formulas were developed for the translation of roll and yawacceleration commands into aerodynamic and thrust-vectoring control deflections. Sample data from theapplication of the method to the control of the High Angle-of-Attack Research Airplane (HARV) areincluded. The method has become known as the pseudo controls technique because of the use ofnormalized control variables (pseudo controls) that command coordinated aerodynamic and thrust-vectoring controls to produce uncoupled roll and yaw moments. The method does not include sensorfeedback or pilot actions feed-forward elements of a control system that determine the requiredaccelerations at any given time. The pseudo control system developed in the present report includes thefollowing key elements:

• Transformation of stability-axis acceleration commands to body-axis acceleration commands.

• Calculation of body-axis control moments needed to produce the required accelerations and tocounter inertial coupling effects.

• Calculation of the body-axis control moments available from coordinated control deflections andthe fractions of these (pseudo controls) required to produce the required moments.

38

• Calculation of the maximum stability-axis roll acceleration possible with the available controlmoments (provided for use in pilot command gain).

• Distribution of roll and yaw pseudo controls to aerodynamic and thrust-vectoring control devices.

• Calculation of interference in the lateral accelerometer output caused by thrust-vectoring andactuated forebody strake control moments (for use in correcting acceleration feedback signals).

• Scheduling thrust-vectoring usage according to effectiveness relative to that of the aerodynamiccontrols.

• Replacing long-term thrust-vectoring commands by aerodynamic control deflections in order torelieve heating loads on exhaust jet turning vanes.

References

1. Matheny, Neil W., compiler: High-Angle-of-Attack Projects and Technology Conference. Volume 1, NASACP-3137, 1992.

2. Barham, Robert W.: Thrust Vector Aided Maneuvering of the YF-22 Advanced Tactical Fighter Prototype.AGARD Conference Proceedings 548: Technologies for Highly Maneuverable Aircraft, March 1994.

3. Nguyen, Luat T.; Arbuckle, P. Douglas; and Gera, Joseph: Progress in Controls Technology for High-Angle-of-Attack Applications. High-Angle-of-Attack Technology, Volume I, CP-3149, NASA Langley Research Center,Hampton, VA, Oct. 30–Nov. 1, 1990, pp. 117–156.

4. Pahle, Joseph W.; Powers, Bruce; Regenie, Victoria; Chacon, Vince; Degroote, Steve; and Murnyak, Steven:Research Flight-Control System Development for the F-18 High Alpha Research Vehicle. NASA TM-104232,1991.

5. Regenie, Victoria; Gatlin, Donald; Kempel, Robert; and Matheny, Neil: The F-18 High Alpha ResearchVehicle: A High-Angle-of-Attack Testbed Aircraft. NASA TM-104253, 1992.

6. Mason, Mary L.; Capone, Francis J.; and Asbury, Scott C.: A Static Investigation of the Thrust Vectoring Systemof the F/A-18 High-Alpha Research Vehicle. NASA TM-4359, 1992.

7. Asbury, Scott C.; and Capone, Francis J.: Multiaxis Thrust-Vectoring Characteristics of a Model Representativeof the F-18 High-Alpha Research Vehicle at Angles of Attack From 0° to 70°. NASA TP-3531, 1995.

8. Bundick, W. Thomas; Pahle, Joseph W.; Yeager, Jessie C.; and Beissner, Fred L., Jr.: Design of a Mixer for theThrust-Vectoring System on the High-Alpha Research Vehicle. NASA TM-110228, 1996.

9. Murri, Daniel G.; Shah, Gautum H.; DiCarlo, Daniel J.; and Trilling, Todd W.: Actuated Forebody StrakeControls for the F-18 High-Alpha Research Vehicle. J. Aircr., vol. 32, no. 3, May–June 1995.

10. Erickson, Gary E.; and Murri, Daniel G.: Wind Tunnel Investigations of Forebody Strakes for Yaw Control onF/A-18 Model at Subsonic and Transonic Speeds. NASA TP-3360, 1993.

11. HARV Control Law Design Team: Design Specification for a Thrust-Vectoring, Actuated-Nose-Strake FlightControl Law for the High-Alpha Research Vehicle. NASA TM-110217, 1996.

39

12. Hoffler, Keith D.; Brown, Philip W.; Phillips, Michael R.; Rivers, Robert A.; Davidson, John B., Jr.; Lallman,Frederick J.; Murphy, Patrick C.; and Ostroff, Aaron J.: Evaluation Maneuver and Guideline Development forHigh-Alpha Control Law Design Using Piloted Simulation. AIAA 94-3512, Aug. 1994.

13. Ostroff, Aaron J.; Hoffler, Keith D.; and Proffitt, Melissa S.: High-Alpha Research Vehicle (HARV)Longitudinal Controller: Design, Analyses, and Simulation Results. NASA TP-3446, 1994.

14. Murphy, Patrick C.; and Davidson, John B.: A Control Law Design Method Facilitating Control Power,Robustness, Agility, and Flying Qualities Tradeoffs: CRAFT. NASA/TP-1998-208463, 1998.

15. Buttrill, Carey S.; Arbuckle, P. Douglas; and Hoffler, Keith D.: Simulation Model of a Twin-Tail, HighPerformance Airplane. NASA TM-107601, 1992.

16. Messina, Michael D.; Strickland, Mark E.; Hoffler, Keith D.; Carzoo, Susan W.; Bundick, W. Thomas; Yeager,Jessie W.; and Beissner, Fred L., Jr.: Simulation Model of the F/A-18 High Angle of Attack Research VehicleUtilized for the Design of Advanced Control Laws. NASA TM-110216, 1996.

17. Advanced Continuous Simulation Language (ACSL) Reference Manual. Edition 10.0, Mitchell and GauthierAssoc., 1991.

18. Ashworth, B. R.; and Kahlbaum, W. M., Jr.: Description and Performance of the Langley DifferentialManeuvering Simulator. NASA TN D-7304, 1973.

19. Lallman, Frederick J.: Relative Controls Effectiveness Technique with Application to Airplane ControlCoordination. NASA TP-2416, 1985.

20. Lallman, Frederick J.: Preliminary Design Study of a Lateral-Directional Control System Using ThrustVectoring. NASA TM-86425, 1985.

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REPORT DOCUMENTATION PAGE

September 1998 Technical Publication

A Method for Integrating Thrust-Vectoring and Actuated Forebody StrakesWith Conventional Aerodynamic Controls on a High-Performance FighterAirplane

WU 522-22-21-03

Frederick J. Lallman, John B. Davidson, and Patrick C. Murphy

L-17627

NASA/TP-1998-208464

A method, called pseudo controls, of integrating several airplane controls to achieve cooperative operation ispresented. The method eliminates conflicting control motions, minimizes the number of feedback control gains,and reduces the complication of feedback gain schedules. The method is applied to the lateral/directional controlsof a modified high-performance airplane. The airplane has a conventional set of aerodynamic controls, an experi-mental set of thrust-vectoring controls, and an experimental set of actuated forebody strakes. The experimentalcontrols give the airplane additional control power for enhanced stability and maneuvering capabilities while flyingover an expanded envelope, especially at high angles of attack.

The flight controls are scheduled to generate independent body-axis control moments. These control momentsare coordinated to produce stability-axis angular accelerations. Inertial coupling moments are compensated.Thrust-vectoring controls are engaged according to their effectiveness relative to that of the aerodynamic controls.Vane-relief logic removes steady and slowly varying commands from the thrust-vectoring controls to alleviate heat-ing of the thrust turning devices. The actuated forebody strakes are engaged at high angles of attack.

This report presents the forward-loop elements of a flight control system that positions the flight controlsaccording to the desired stability-axis accelerations. This report does not include the generation of the requiredangular acceleration commands by means of pilot controls or the feedback of sensed airplane motions.

F/A-18 High-alpha research vehicle (HARV); Actuated nose strakes for enhanced rolling(ANSER); Fighter aircraft; Flight controls; Airplane control; Control design; Thrust vectoring;Forebody strakes; Forebody controls; High angle of attack; Integrated control

45

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